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Discussion Forum

Que. Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

(∃x)(∀y)[(a(x, y) ∧ b(x, y)) ∧ ¬c(x, y)]

Which one of the following is its equivalent?  
a. (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]
b. (∃x)(∀y)[(a(x, y) ∨ b(x, y)) ∧¬ c(x, y)]
c. ¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]
d. ¬ (∀x)(∃y)[(a(x, y) ∨ b(x, y)) → c(x, y)]
Answer:¬ (∀x)(∃y)[(a(x, y) ∧ b(x, y)) → c(x, y)]
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